In my opinion there are two main approaches to jazz improvisation. The first one is the good old and natural thing: play what someone played before. Phrases tend to be one or two measures long. Than combine them in a new fashion
The second, also my favorite, is: analyze what someone played before and then „derivate“ your own exercises from it. It should be reduced to four-tone phrases.
The first approach was mainly used by jazz musicians in the tradition of swing and bebop, like Louis Armstrong, Charlie Parker, Sonny Stitt. Because the instrument’s physics require a very exact prehearing of your phrases most of the serious trumpet players used and actually using this approach. I like the traditional sound of this thing and the fact that you have to listen to all these cats and play very hip shit. With this comes a good feeling for bounce and sound. The fact I don’t like is the more repetitive sound and less freedom what to play.
The second approach is a more intellectual one. It’s based mostly on four-tone phrases. This approach was used f.e. by Sonny Rollins, John Coltrane and is used by many modern players today. A very popular version of this approach is Coltrane’s set of four-tone pattern in the range of a fifth which he used very extensively over tunes like Giant Steps.
Most of today’s jazz players using various mixes of these two approaches. In the following posts I will write mainly about the second approach because it’s the way I practice.